This　paper　mainly　deals　with　the　kinematic　analysis　and　performance　comparisons　of　three　redundant　parallel　mechanisms　for　fracture　reduction　surgery.　First,　two　novel　kinematically　redundant　parallel　mechanisms　for　surgical　robots　are　proposed　based　on　the　Gough–Stewart　parallel　platform.　The　kinematics　of　the　three　mechanisms　are　established,　and　their　workspaces　are　analyzed.　The　analysis　result　shows　that　the　workspace　volume　of　the　redundant　mechanism　can　be　improved　by　71.6%.　Second,　considering　the　stroke　of　redundant　actuators,　the　effects　of　the　slider　strokes　on　the　position　and　orientation　workspaces　are　obtained.　The　multi-objective　optimization　method　is　used　to　optimize　the　geometric　parameters　of　the　three　mechanisms.　Third,　the　singularities　of　the　three　redundant　parallel　mechanisms　are　compared　based　on　the　dimensionally　homogeneous　Jacobian　matrix.　Finally,　experiments　are　conducted　to　verify　the　effectiveness　of　the　performance　comparison　methods　in　this　paper.　©　2023　Elsevier　Ltd